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Question

The tangent of the graph of the function y = f(x) at the point with abscissa x = 1 form an angle of π6 and at the point x = 2 an angle of  π3 and at the point x = 3 angle of 
π4. The value of  31f(x)f"(x)dx+31f"(x)dx(f"(x)) is suppose to be continuous) is
  1. None of these
  2. 43133
  3. 433
  4. 3312


Solution

The correct option is D 3312
f(x)=n(1+x)n1,f"(x)=n(n1)(1+x)n2fn(x)=n!,fn(0)=n!1+n+n(n1)2!+....+n!n!=nC0+nC1+nC2+...+nCn=2n

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